Solve part B through F In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdfbelow.0 ≤ y < 5f(y) =#5 ≤ y ≤ 10250y <0 or y> 10(a) Sketch a graph of the pdf of Y.f(y)f(y)f(y)f(y)0.200.200.200.20k0.150.150.150.15IZUIZN0.100.100.100.100.050.050.050.05Vyy246810O24681024681046810(b) Verify thatf(y) dy = 1.+ [° F(x)[Andy=[105= 1/2+(c) What is the probability that total waiting time is at most 3 min?(d) What is the probability that total waiting time is at most 9 min?(e) What is the probability that total waiting time is between 3 and 9 min?(f) What is the probability that total waiting time is either less than 4 min or more than 7 min?

Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 25% osy<5 f(y) = 5 sys 10 0 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20k 0.20 0.20 0.20k 0.15 0.15 0.15 0.15 ÍZKEZA. 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 y 2 4 6 O 8 10 2 4 8 O 6 10 8 O 2 4 6 10 2 4 6 8 10 (b) Verify that t [*^ Ry) dy = 1. 10 f(y) dy= 5 525 (c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 9 min? 25